Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (3): 801-826.

• Articles •

### HIGH-ORDER NUMERICAL METHOD FOR SOLVING A SPACE DISTRIBUTED-ORDER TIME-FRACTIONAL DIFFUSION EQUATION

Jing LI1, Yingying YANG1, Yingjun JIANG1, Libo FENG2, Boling GUO3

1. 1. School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, China;
2. School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD 4001, Australia;
3. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
• Received:2019-11-26 Revised:2020-09-24 Online:2021-06-25 Published:2021-06-07
• Contact: Jing LI E-mail:lijingnew@126.com
• About author:Yingying YANG,E-mail:1720719892@qq.com;Yingjun JIANG,E-mail:jiangyingjun@csust.edu.cn;Libo FENG,E-mail:fenglibo2012@126.com;Boling GUO,E-mail:gbl@iapcm.ac.cn
• Supported by:
The first author is supported by the Natural and Science Foundation Council of China (11771059), Hunan Provincial Natural Science Foundation of China (2018JJ3519) and Scientific Research Project of Hunan Provincial office of Education (20A022).

Abstract: This article proposes a high-order numerical method for a space distributed-order time-fractional diffusion equation. First, we use the mid-point quadrature rule to transform the space distributed-order term into multi-term fractional derivatives. Second, based on the piecewise-quadratic polynomials, we construct the nodal basis functions, and then discretize the multi-term fractional equation by the finite volume method. For the time-fractional derivative, the finite difference method is used. Finally, the iterative scheme is proved to be unconditionally stable and convergent with the accuracy $O(\sigma^2+\tau^{2-\beta}+h^3)$, where $\tau$ and $h$ are the time step size and the space step size, respectively. A numerical example is presented to verify the effectiveness of the proposed method.

CLC Number:

• 35R11
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